Just came across an interesting question around strategic betting and was wondering if I would be able to get your thoughts on this one:
You can deposit \$1000 on a blackjack website and they will give you \$1000 of credit to match. You can only withdraw once you have bet a total of \$10000 on blackjack hands. Suppose that you expect 90c per \$1 of play. What is the optimal betting strategy?
Here I thought about the fact that if you were to bet a \$1 each time of play, you will be left with nothing (on average) after 10000 rounds as you lose money per round. This is also true if you decide to bet \$2 each round, and same goes for \$3 etc. Therefore, you should bet the whole \$1000 and if you win, you can safely bet \$1 each round to reach the \$10000 target.
Not sure if this is correct so I'm wondering what your thoughts are on this. Thanks!